That is possibly correct, in that the border towns are within the 'zona frontera', where you don't need a visa for 72 hours and your car doesn't need an 'importada temporal' for a short visit. However, living there might change things, especially if you were to try to buy a home.
Remember that the lien holder of the car will not want you to take the car out of the USA and you will have to get a letter of permission from them. If you were to lose the car in Mexico, for any reason, you could be putting yourself in a very tight spot. So, my suggestion is to pay off the loan and move anywhere you like in Mexico. If that isn't possible, your plan to move may be premature.